## Tuesday, February 05, 2019

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I thought BV meant Bill Vallicella!

Sorry, Bill, bad joke . . .

Jeffery Hodges

* * *

Hi Jeff,

Great to hear from you. Are you on Facebook?

Just finished listening to Trump's State of the Union address. Impressive. He really rose to the occasion.

Best to you and yours,

Bill

A few points. First, the schemata I set out in my previous comments were not disquotational.

TRUE: S says that p and p
FALSE: S says that p and not-p

I used a ‘that’ clause to specify what S says. Of course there is a schema, but that is because ‘p’ is a placeholder for any meaningful sentence.

Second, I note you have only two schemata, whereas Aristotle gives 4. I suppose two are sufficient on the assumption that ‘p’ could stand in for a negated sentence, e.g. ‘grass is not green’. So if S says that grass is not green and it is not the case that grass is not green, then S speaks falsely.

Third, your schema is

DS: p is true iff p.

This is not quite the same as my schema, as is obvious from above. Let’s assume it doesn’t matter for the moment.

>> This will NOT work if negation can only be explained in terms of falsehood. For then we would enter an explanatory circle of embarrassingly short diameter. The negation of p is the proposition that is true iff p is false and false iff p is true. To explain the logico-syntactic notion of negation we have to reach for the semantic notions of truth and falsehood. But then falsehood cannot be exhaustively understood or reduced to negation.<<

But as I have argued elsewhere, we can define negation without reaching for the notions of truth and falsity. Assume that the notion of ‘all possible situations’ is coherent, and suppose it is coherent for any proposition ‘p’ to map onto a subset of that set. Then ‘not p’ maps onto the complement. The question is whether the very idea of a complement or of a subset covertly appeals to the concept of negation. But then that suggests that negation is a primitive indefinable concept, rather than what you are claiming (namely that it is truth and falsity which are primitive).

>> Are there counterexamples to (DS)? It seems to fail right-to-left if 'Sherlock Holmes is a detective' is plugged in for 'p' on the RHS of (DS). Arguably, Holmes is a detective, but it is not true that Holmes is a detective.<<

No. It is true that Conan Doyle said that Sherlock Holmes is a detective. It is not true, understood strictly and literally, that Sherlock Holmes is a detective.

Bill, can you elaborate on a couple of things? First, how is DS-F a consequence of DS?

Second, you say "But this works only if falsehood can be adequately explained in terms of the merely logical operation of negation." I don't see where this comes from unless you are thinking that DS-F is to be taken as a definition of falsehood, but DS-F is symmetrical, so it could just as easily be taken as a definition of negation, or for that matter it could be taken as an axiom that is not a definition at all.

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